I ran a few forums before (they've been closed for years) and a lot of the members requested this but once it was in place it killed the site. New members stopped joining and the old members stopped posting. Its a strange balance for a site owner to weigh the need for privacy and the SEO bringing in new members and after it killed not one but two of my forums if I ever decide to run another forum I wouldn't do it.

So if its really private I think DS has a "sensitive topics" sub forum you can subscribe to.